(x+3)(x+6)=119

Solution for (x+3)(x+6)=119 equation:

Simplifying
(x + 3)(x + 6) = 119

Reorder the terms:
(3 + x)(x + 6) = 119

Reorder the terms:
(3 + x)(6 + x) = 119

Multiply (3 + x) * (6 + x)
(3(6 + x) + x(6 + x)) = 119
((6 * 3 + x * 3) + x(6 + x)) = 119
((18 + 3x) + x(6 + x)) = 119
(18 + 3x + (6 * x + x * x)) = 119
(18 + 3x + (6x + x2)) = 119

Combine like terms: 3x + 6x = 9x
(18 + 9x + x2) = 119

Solving
18 + 9x + x2 = 119

Solving for variable 'x'.

Reorder the terms:
18 + -119 + 9x + x2 = 119 + -119

Combine like terms: 18 + -119 = -101
-101 + 9x + x2 = 119 + -119

Combine like terms: 119 + -119 = 0
-101 + 9x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '101' to each side of the equation.
-101 + 9x + 101 + x2 = 0 + 101

Reorder the terms:
-101 + 101 + 9x + x2 = 0 + 101

Combine like terms: -101 + 101 = 0
0 + 9x + x2 = 0 + 101
9x + x2 = 0 + 101

Combine like terms: 0 + 101 = 101
9x + x2 = 101

The x term is 9x.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9x + 20.25 + x2 = 101 + 20.25

Reorder the terms:
20.25 + 9x + x2 = 101 + 20.25

Combine like terms: 101 + 20.25 = 121.25
20.25 + 9x + x2 = 121.25

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 121.25

Calculate the square root of the right side: 11.011357773

Break this problem into two subproblems by setting 
(x + 4.5) equal to 11.011357773 and -11.011357773.

Subproblem 1
x + 4.5 = 11.011357773

Simplifying
x + 4.5 = 11.011357773

Reorder the terms:
4.5 + x = 11.011357773

Solving
4.5 + x = 11.011357773

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = 11.011357773 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = 11.011357773 + -4.5
x = 11.011357773 + -4.5

Combine like terms: 11.011357773 + -4.5 = 6.511357773
x = 6.511357773

Simplifying
x = 6.511357773

Subproblem 2
x + 4.5 = -11.011357773

Simplifying
x + 4.5 = -11.011357773

Reorder the terms:
4.5 + x = -11.011357773

Solving
4.5 + x = -11.011357773

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = -11.011357773 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = -11.011357773 + -4.5
x = -11.011357773 + -4.5

Combine like terms: -11.011357773 + -4.5 = -15.511357773
x = -15.511357773

Simplifying
x = -15.511357773

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.511357773, -15.511357773}